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As discussed in Maseches Rosh Hashanah, if two witnesses saw the new moon, they'd go to Beis Din to testify they saw it and Beis Din would then declare when Rosh Chodesh would be.

But what if these witnesses were found to be eidim zomememim? An initial assumption we could make is to say it falls into the general criteria taught in Makkos 2a of what to do when we can't really apply "v'aseesem lo ka'asher zamam":

ויש עדים זוממין אחרים שאין עושין בהן דין הזמה כל עיקר אלא מלקות ארבעים

And there are other conspiring witnesses with regard to whom the court does not apply the halakhot governing the cases of conspiring testimony at all, and they do not receive the punishment they sought to have inflicted. Rather, they receive forty lashes.

But... can we actually apply this reasoning to witnesses for a new moon? We can make a distinction that Makkos 2a is an eidus that will inflict damage in someone, either literally or financially.

However, witnesses for a new moon are NOT testifying against a person but rather about an event and (apologies if I may be mistaken), but even if Beis Din decrees what is literally the wrong day, Beis Din's decree wins out even over the actual metzius- ie even if the witnesses were liars it's irrelevant since we follow what BD says and l'maaseh it would turn out they wouldn't be harming anyone.

B'kitzur: what would happen the case of eidim zomemim for a new moon, and if they get a punishment- what would it be?

According to Rabbi Akiva Eiger, (Shu"t RA"E Mahadura Kama 176, cited here) they are not punished by the hand of man:

וגם משום מלקות, נראה דלא לקו, דלא שייך בזה 'לא תענה ברעך' דהא לא העידו כלל על רעהו להפסידו בשום דבר

And also with regard to lashes, it would appear that they were not lashed, for [the verse - Exodus 20:12] "though shalt not testify against thine fellow [false testimony]" is not applicable [in this case], for indeed they did not testify against [their] fellow abouth anything

Let me explain the logic of the accepted answer (unfortunately, it's just "it would appear that"):

1. 
   

   As you mentioned, unlike other cases where the witnesses actually determine the situation (like Kiddushin or murder) and we don't know what happened without their testimony, in Rosh Chodesh the situation is exactly the opposite - the Beis Din makes the calculations and considerations in advance and decides on when the Rosh Chodesh will be, and they invite the witnesses only to "follow the protocol" or a אסמכתא if you like.

   
   
   

   It is clear from the Gemmorah that the witnesses are completely optional and the court is not really "obligated" to accept their testimony, therefore, they are exempt from punishment.

   
   
   

   I remind you that a court is allowed to give lashes just for anything - עונשים שלא מן הדין, therefore the lashes can be applied to punish the witnesses for obstruction of justice etc, but not for their false testimony.

   
   



2. The fact they were זוממין does not invalidate the fact of the new Moon, they could perfectly see it from another place. Seeing the Moon does not require כוונה or התראה, so even sitting with friends and gazing at the Moon is sufficient.